Geometric analysis on non-compact and singular spaces

Singularities are omnipresent in sciences and in everyday life, from breaking waves to black holes in Einstein's theory of relativity. Geometric analysis provides the right language to study them in many situations, notably in physics and engineering, but also in medical imaging, in geology or even in biology. In this project, we will investigate various problems using three different ways to look at singularities: geometric scattering theory, spectral invariants and cohomology theories. In doing so, we will develop novel techniques involving manifolds with corners, microlocal analysis and Ricci flow that will lead to new results and striking relationships between geometry and spectral analysis on non-compact and singular spaces.